Hello again. Thanks for the quick reply. The J5 multimedia USB adapter looks to be a third-party product. Do you mean to say that you purchased it at an Apple Store? I still suspect that this issue is caused by insufficient USB power being delivered to your SuperDrive. This can happen regardless of the manufacturer of the drive, computer, or adapter you are using. External CD and DVD drives, such as the SuperDrive, require a certain amount of power to function properly.
With this in mind, do you also know how old your Apple SuperDrive is? Some of the adapters offered by Apple unfortunately do not work Apple SuperDrives that were manufactured before Fall 2010. This is the only Apple listed on the SuperDrive page that is not listed as incompatible with older SuperDrives.